Density & Pressure

Definition

• Density (ρ) is the mass per unit volume of a material
• It tells you how tightly the matter in a substance is packed together. Two objects of identical size made from different materials can have very different masses; the denser one feels heavier

The density equation

ρ = m / V

• where:
  • ρ = density (kg/m³ in SI units; sometimes quoted in g/cm³)
  • m = mass (kg or g)
  • V = volume (m³ or cm³)
• Useful rearrangements:
  • m = ρ × V (how much a fixed volume of a known material weighs)
  • V = m / ρ (the volume occupied by a known mass of a known material)

Comparing states of matter

• For the same substance, density generally falls as you go from solid → liquid → gas:
  • Solid: particles packed tightly in a fixed lattice. Highest density of the three states
  • Liquid: particles still touching but free to slide past each other. Slightly less dense than the solid (water is the famous exception: ice floats on water because solid water is less dense than liquid water)
  • Gas: particles spread far apart with mostly empty space between them. Density is typically about a thousand times smaller than the liquid or solid forms

Units conversions

• SI density is kg/m³, but g/cm³ is also very common. The conversion:
  • 1 g/cm³ = 1000 kg/m³ (water has a density of 1.0 g/cm³ = 1000 kg/m³)
• Useful reference densities:
  • air at sea level ≈ 1.2 kg/m³
  • water ≈ 1000 kg/m³
  • aluminium ≈ 2700 kg/m³
  • iron ≈ 7900 kg/m³
  • lead ≈ 11 300 kg/m³